Dynamic properties of pH-dependent structural organization of the amyloidogenic β-protein (1-40)

Abstract

The structural organization of the amyloidogenic β-proteins containing 40 amino acid residues (Aβ40) was studied by the high temperature molecular dynamics simulations in the acidic (pH~3) and basic (pH~8) pH regions. The obtained data suggest that the central Ala21-Gly29 segment of Aβ40, can adopt folded and partially unfolded structures. At the basic pH, this segment forms folded structures, stabilized by electrostatic interactions and hydrogen bonds. At the acidic pH, it forms partially unfolded structures. Two other segments flanking to the central segment exhibit the propensity to adopt unstable inter-converting α-helical, 310-helical and turn-like structures. One of these segments is comprised of the Ala30-Val36 residues at both of the considered pHs. The second segment is comprised of the Glu11-Phe20 at the basic pH and of the Glu11-Val24 residues at the acidic pHs. The revealed pH-dependent structuration of the Aβ40 allowed us to suggest a possible scenario for initial Aβ aggregation.  According to this scenario, the occurrence of the partially unfolded states of the Ala21-Gly29 segment plays main role in the Aβ oligomerization process.

Introduction

Amyloidogenic, natively unfolded β-protein (amyloid-β or Aβ), consisting of 40 or 42 amino acid residues (referred as Aβ40 or Aβ42, correspondingly), is the major component of the amyloid deposits in the brains of patients with Alzheimer's disease (AD).1,2 This protein can form self-aggregated complexes containing fibrilar and non-fibrilar structures that are neurotoxic and responsible for AD pathogenesis.3–5 A better understanding of the formation of the amyloid oligomers and protofibril is crucial for the rational design of new therapeutic strategies to prevent Aβ aggregation into neurotoxic structures and, perhaps, to treat AD.

Solid state NMR experiments6–9 suggest that a “cross-β supra-molecular” structure of Aβ fibrils is formed in vitro from a core of the elongated β-sheets. Attempts to find structural reorganizations of the Aβ monomers that precede their folding into the predominantly β-stranded structures did not reveal a single pathway.10–30 These studies have shown that, the Aβ monomers may contain the α-helix, β-strand or collapsed-coil structural components, as well as a mixture of the α-helix/β-strand or a-helix/collapsed-coil structural components at the early stages of aggregation. Recent works31–34 suggest that partial unfolding of the somehow initially folded Aβ(21–30) segment may be necessary for the subsequent fibrilization of the Aβ monomers. Overall, the existing experimental data suggest that the Aβ monomers should undergo structural reorganization events to approach an intermediate structural state required for the initiation the Aβ oligomeric and protofibril aggregation. The mechanisms of these structural reorganizations have not been fully discovered yet.

In this work, we have focused on studying how the pH of the surrounding media can influence the structural organization of Aβ monomers. The rationale behind this work is based on an in vitro observation showing that the oligomeric and protofibril aggregation of the Aβ protein can be induced by the pH and temperature changes.13,35–39 It was demonstrated13,38,39 that the aggregation rate of the Aβ fibril formation is much faster at the acidic pH compared to the neutral and basic pHs. Data obtained by solid state NMR spectroscopy9 and atomic force microscopy experiments40–42 also showed pH-dependent structural alterations of the Aβ monomers. On the other hand, pH values determine protonated and deprotonated states of the amino acid residues having ionogenic groups. Since there are many residues with the ionogenic groups in the Aβ sequence, the pH changes can shift the balance of the Aβ intra-protein electrostatic interactions that, in turn, can change the structural propensities of the monomers and alter the process of Aβ oligomerization and fibrilization.

To elucidate the role of electrostatic interactions in the structural organization of Aβ monomers, we performed the high temperature (HT) molecular dynamics (MD) simulations of the Aβ40 monomer at the acidic (pH ∼ 3) and basic (pH ∼ 8) pHs, which were referred to as pH 3 and pH 8, correspondingly. The HT simulations are used to increase conformational sampling and to diminish the probabilities that a peptide or unstructured short protein will be trapped in one or a few local-minimum-energy states. The HT molecular dynamic simulation protocols were found to be useful in many studies.43–49

By combining the HT simulations data with known experimental data, we have proposed a model of the pH-dependent structural organization of the Aβ monomer. This model suggests that electrostatic interactions within the central Ala21-Gly29 segment play a crucial role in the ability of Aβ40 to commence or escape oligomerization and fibrilization processes. The proposed model provides an explanation of some experimental data on the Aβ oligomerization and fibrilization. The model also clarifies the nature of the structural changes caused by several well-known pathological mutations of the Aβ proteins and sheds light on a mechanism that can trigger the initiation of fibril formation.

Results and Discussions

To estimate a general dynamic behavior of the Aβ40 structure during the time of the full simulations, the radii of gyrations (Rg) were calculated using coordinates of the heavy backbone atoms (Cα, C, N) of the whole Aβ40 presented in the MDA₃, MDA₈, MDB₃ and MDB₈ trajectory files (see Methods). The dynamics behavior of the corresponding values of the Rg (RgA₃, RgA₈, RgB₃ and RgB₈, respectively) is shown in Figure 1A and B. As can be seen from Figure 1A, the RgA₈ values are changing during a rather short time from the starting values of ∼15 Å to the average value, <RgA₈> ≈ 11.6 ± 1.8 Å (after ∼150 ps), while the RgB₈ are started from the values of ∼35 Å and approach (after about 2 ns) very similar values, <RgB₈> ≈ 11.5 ± 2.0 Å. A similar picture was observed for the behavior of the Aβ40 at pH 3 (Fig. 1B). Starting from the values of ∼15 Å and ∼35 Å, the corresponding RgA₃ and RgB₃ also approach very similar average values: <RgA₃> ≈ 10.7 ± 1.2 Å (after ∼300 ps) and <RgB₃> ≈ 10.75 ± 1.3 Å (after ∼4 ns).

Therefore, during the MD simulations, the average values of the radius of gyration of the Aβ40 monomer are dependent on the considered pHs, but not from the choice of the initial structure. Thus, the structural behavior of Aβ40 can be viewed as a behavior of a flexible, unstable system, adopting several pH-dependent structural formations (Fig. 1).

To analyze the pH-dependent structural formations of Aβ40, the detailed structural analysis of the conformers, selected at the last 10 ns of the performed simulations, was carried out. For this purpose, data collected in the RSA₈, RSA₃, RSB₈ and RSB₃ files (see Methods) were used. Analysis of the formation of secondary structure elements (SSE) for RSA₃ and RSA₈ as well as RSB₃ and RSB₈ structural sets showed that at both pHs the amino acids of the Aβ40 are mainly involved in the formation of α-helixes, 3₁₀-helixes and β-turns and random coils (Tables 1 and 2). It should be noted that the hydrogen bonded β-strand structure, which was absent in the considered structural sets, and two other structures, isolated β-strand and π-helix, that appeared very rarely in these sets, were omitted from this table. To analyze whether the structural propensity (SP) of the amino acid residues of Aβ40 depend on initial starting structures (A and B) during MD simulations, we calculated the correlation coefficients (R) between SP of amino acid residues within several segments of the Aβ40 sequence to be involved in the formation of the α-helix, 3₁₀-helix and β-turn structures as well as the random coil obtained for two initial structures at the same pH (Tables 1 and 2). We found that during the last 10 ns of the A and B runs (see Methods) the corresponding amino acid residues within the Glu11-Val39 segment have rather strongly correlated propensity to form the α-helix, 3₁₀-helix and random coil structural elements: the correlation coefficients, R, are 0.92, 0.86 and 0.95 (respectively) at pH 8 and 0.87, 0.91 and 0.86 at pH 3. Smaller, but remarkable correlations between the SP of these residues to belong to the β-turn structures were also observed (R = 0.73 at pH 8 and R = 0.6 at pH 3). This analysis suggests that, during the last 10 ns of MD simulations at the given pH, the residues within the Glu11-Val39 segment for both runs have similar tendency to be involved in helix- and coil-like structural motifs. This result suggests that the amino acid residues from the Glu11-Val39 sequence at the given pH exhibit similar structural behavior independent from the initial structures.

In contrast to the Glu11-Val39 segment, the residues within the Ala2-Tyr10 segment exhibited low or moderate ability (data are not shown) to be involved in the formation of the α-helix, 3₁₀-helix and random coil at pH 3 (R = 0.6, 0.86 and 0.64, respectively). At pH 8 such a correlation is absent (R = −0.3, −0.4 and −0.1, respectively). The similarities in adopting the β-turn structures were found to also be absent at pH 8 (R = 0.1) and low at pH 3 (R = 0.6). Thus, we concluded that the structural preferences of the Ala2-Tyr10 segment significantly depend not only on pH, but also on the initial structure. Because the first 10 residues in Aβ40 were found to be structurally disordered in the fibrilles6,8 and are likely not important for aggregation,8 we did not perform any additional analysis of this segment.

Figure 2 presents the SP of the amino acid residues of the Aβ40 at the last 10 ns of the MD simulations performed for A and B initial structures at pH 8. This figure suggests the presence of three distinct zones exhibiting different SP along the Aβ40 core domain (Glu11-Val36). These three zones are formed from the following residues: Glu11-Phe20 (Zone I), Ala21-Gly29 (Zone II) and Ala30-Val36 (Zone III). At both pHs, the residues within Zones I and III demonstrate propensity to be involved in the formation of a-helix, 310-helix and β-turn structural motifs. This is in contrast to Zone II, where the residues at pH 8 do not exhibit a significant propensity to be involved in forming any of the considered types of secondary structures.

Structural preferences of the amino acid residues within Zone I and Zone III.

As can be seen from Tables 1, 2 and Figure 2, the SP of the amino acid residues within Zone I (Glu11-Phe20) and Zone III (Ala30-Val36) of the Aβ40 core domain can be described as inter-converting structural formations. These formations include helical, β-turn and random coil structural motifs at both pH 3 and pH 8. To better understand how the choice of the initial structure influences the structural preferences of the amino acid residues within Zone I and Zone III at the considered pH, we performed the structural cluster analysis described below. This analysis was carried out using the RS₈ and RS₃ datasets, which were obtained by combining the RSA₈ and RSB₈ as well as RSA₃ and RSB₃ sets taken at pH 8 and pH 3, correspondingly. Thus, within each of the combined sets, RS₈ and RS₃, 1,000 MD generated conformers were analyzed. We performed structural cluster analyses of the following five tetrapeptide segments: Glu11-His14, His14-Leu17 and Leu17-Phe20 as well as Ala30-Gly33 and Gly33-Val36. In this analysis, the value of RMSD ≤ 1.0 Å (for the heavy backbone atoms) for the segments was taken as a criterion of a structural similarity (see Methods). To test whether the average structures of the clusters obtained under the high temperature MD simulations are persistent at low temperatures, these structures were energy-minimized and compared (by RMSD calculated for the backbone heavy atoms) with the “ideal” α-helical, 3₁₀-helical, π-helical and β-strand structures (as described in Methods). The results of these comparisons are summarized in Table 3. Data in this table suggest that at the given pH the most preferable helix-like structuration within segments belonging to Zone I and Zone III, is independent of the choice of the initial structure (or this dependence is very weak). The helical structuration of the core domain found in the present work is consistent with the results of MD simulations performed at room temperature for the Aβ(10–35) peptide in aqueous solution at the neutral pH.61 In that work it was shown that the Aβ(10–35) peptide predominantly adopts helix-like structures, while the propensities to adopt β-strand-like structures were much weaker. Helical formations of the Aβ monomer and its fragments at neutral and low pHs were also found in other works.10,17,20,24,30,62

It should be noted that a general tendency of the peptide segments within Zone I and Zone III to adopt the helix-like formations is only weakly dependent on the considered pHs (Tables 1–3). These data taken together with the data obtained at neutral pHs in the aforementioned works suggest that the protonation or deprotonation of the Aβ histidines (His6, His13 and His14) apparently do not change the general tendency of the residues within Zones I and III to preferably adopt helical conformations.

Structural preferences of the central Zone II comprised of the Ala21-Gly29 residues.

As can be seen from Tables 1 and 2, the structural preferences of the central Ala21-Gly29 segment are pH dependent. To better understand how pH changes influence the structural preferences of this segment we performed a cluster analysis of four structural sets, RSA₈, RSA₃, RSB₈ and RSB₃, corresponding to A and B initial starting structures. Each average structure of the obtained structural clusters of the Ala21-Gly29 segment was energy-minimized using the procedure described in Methods. We found (see below) that the structural shapes of the segment obtained at the high temperature are persistent after the energy minimization and are very similar for both initial structures. Therefore, we only present data obtained for the initial structure B in Table 4.

The performed analysis suggests that, at pH 8, almost all of the structures formed by the residues belonging to the Ala21-Gly29 segment can be assigned to four clusters shown in Table 4. As can be seen from this table, cluster 1 is comprised of about 84% of the considered structures, while three other clusters are low populated. The minimized and non-minimized average structures had RMSD ∼1.0 Å for the heavy backbone atoms. The C_α-trace of the energy-minimized average structure corresponding to the most populated cluster is shown in Figure 3. As can be seen from this figure, the Ala21-Val24 residues of this segment form the hook-shaped structures, while the Gly25-Gly29 residues form the bend-shaped structures. Overall, the fold of the whole Ala21-Gly29 segment resembles a distorted omega-like (Ω) structure. We called the state in which the Ala21-Gly29 segment forms compact, Ω-shaped structures, the stable (or folded) state. The states in which the corresponding residues form structures grouped into the low populated clusters (Table 4, clusters 2, 3 and 4), we called the meta-stable states of the Ala21-Gly29 segment.

The structures formed by the Ala21-Gly29 segment at pH 3 are grouped in many relatively low populated clusters (Table 4). None of these clusters contains the majority of the corresponding structures. Therefore, at this pH, the Ala21-Gly29 segment exists in several meta-stable states, and does not exhibit the propensity to be in a stable state. The structures in the meta-stable states differ significantly from those in the stable state. Two factors are responsible for this. First, the Ala21-Val24 part of the central segment exhibits the propensity to adopt the α-, 3₁₀-helix and β-turn-like structures (with the RMSDs equal to 0.53, 0.47 and 0.6 Å, respectively). The second factor is that the orientations of the Ala21-Val24 structures relative to the bend-shaped structures typical for the Gly25-Gly29 segment are significantly different from the orientation taking place in the Ω-shaped structures. Internal conformational flexibility of the central segment at the Gly25 position is associated with the varieties of its orientations taking place in the meta-stable states.

It is important to note that in addition to the aforementioned differences in structural preferences exhibited by the residues belonging to the Ala21-Gly29 segment, there are also some commonalities in the structural behavior of this segment at pH 8 and pH 3. In fact, at both pHs, the Gly25-Gly29 residues adopt similar bend-folded structures. As a part of these folded structures, the Gly25-Lys28 residues form the turn-like structures resembling the β-turn I type structures63 with a smaller distortion at pH 3 and a larger distortion at pH 8. At both pHs, there is also a similarity between the secondary structure elements adopted by the Ala21-Val24 residues in meta-stable states (for example, see clusters 4, 5, 6 and 8 in Table 4). Further, at both pHs the Gly29 residue exhibits some conformational flexibility. Finally, at the considered pHs, remarkable conformation flexibility of the central segment at the Gly25 position was also found in the meta-stable states.

Overall, the performed analysis suggests that at pH 8 the central Ala21-Gly29 segment prefers to be in the stable state, in which it adopts the compactly-folded, Ω-shaped structures. In rare cases, however, this segment can also be observed in the partially unfolded, meta-stable states (see Table 4). In these states the Ala21-Val24 residues adopt β-strand- and helix-like structures different from the hook-shaped structures adopted by these residues, when the central segment is in the folded state. At pH 3, the central segment exists in meta-stable, partially-unfolded states, in which the Ala21-Val24 residues prefer to adopt α-, 3₁₀-helix and turn-like structures. In the folded and partially-unfolded states, the Gly25-Gly29 residues form similar bend-shaped structures.

The revealed structural behavior of the central Ala21-Gly29 segment of the Aβ proteins can explain the pH-related dependences of the attractive forces between two Aβ proteins brought in close proximity in atomic force microscopy (AFM) experiments.40,42 These experiments have shown a non-linear, sigmoidal functional relationship between the attractive forces and pH magnitudes. These forces were found to be minimal in the wide range of the basic pH and increased significantly at the acidic pH. This can be interpreted in the following way. Our MD simulations data showed that at pH 3 the central Ala21-Gly29 segment of Aβ40 forms the partially unfolded structures and has a flexible structure associated with inter-conversions of α-, 3₁₀-helix and β-turn structural modes (Table 4). At pH 8, however, this segment prefers to be in the stable state, in which it adopts the compactly-folded, Ω-shaped structures. Thus, at pH 3 the Aβ core domain exhibits a more flexible structuration compared to its relatively rigged, Ω-shaped structure at pH 8. It is clear that when Aβ proteins are brought together in close proximity in enough random orientation, one relative to another, they have a greater ability to form a larger number of intermolecular contacts, when each of these molecules has higher conformational flexibility. Such an effect is consistent with a flexible protein binding mechanism manifested by the fly-casting effect.64 Thus, the flexible structuration of the Aβ at pH 3 in conjunction with the hydrophobicity effect65 induces further collapse of a larger number of the hydrophobic residues of the interacting proteins and promotes their hydrophobic assembly. Therefore, we suggested that an increase of the attractive forces between two Aβ proteins measured by the AFM at the acidic pH is due to increasing the number of the inter-protein hydrophobic contacts at this pH compared to the ones at the basic pH. In other words, the increase of the attractive forces between two Aβ proteins measured by AFM at the acidic pH compared to basic pH40,42 reflects the difference in the inter-protein hydrophobic interactions at these pHs.

Physicochemical nature of the folded state of the Ala21-Gly29 segment.

To determine the features of forming the Ω-shaped structures, we analyzed the possible nets of hydrogen bonds (H-bonds) and the residue-residue contacts within the Ala21-Gly29 segment at pH 8. For this purpose, the MDB₈ and MDA₈ trajectory files were utilized. The 6.5 Å cutoff distances between the centers of mass of the side chains were used as the criterion for finding the contacting residues.66 The nets of H-bonds and sets of the residue-residue contacts stabilizing the Ω-shaped structures at pH 8 were found to be very similar in both runs. Therefore, below we present the results obtained by the analysis of only one trajectory file, namely MDB₈.

Our analysis showed that when the Ω-shaped structures are formed, the side-chains of the Lys28 and Glu22 residues, as well as the Lys28 and Asp23 residues are close to each other. At pH 8 these structures are stabilized by the network of the H-bonds, formed between the ionogenic groups of Glu22 and Lys28, as well as between the ionogenic group of Asp23 and backbone NH groups of the Val24-Gly29 segment (Table 5 and Fig. 4). In some cases, the H-bonds between the ionogenic group of Asp23 and the polar OH group of the Ser26 side-chain were also observed (Table 5). Our analysis of the distances between the heavy atoms (CD and NZ) of the Glu22 and Lys28 side-chains in the MD₈ trajectory showed that around 70% of MD time this distance was less than 7.0 Å. This suggested that at pH 8, even without the Glu22-Lys28 salt-bridge formation, the long-range ion pair67 between the ionogenic groups of these residues takes place and facilitates the formation of the Ω-shaped structures. It should be noted that the revealed network of the H-bonds and the formation of the Glu22-Lys28 ion pair are well consistent with the data obtained by replica exchange MD simulations performed for the Aβ(21–30) and Aβ(10–35) fragments at the neutral pH.29,34 Thus, our data, taken together with data obtained by Baumketner et al.29,34 suggest that formation of the Ω-shaped structures can be adopted by the Ala21-Gly29 segment at pH 8 as well as at neutral pHs.

Overall, our data suggested that the favorable electrostatic interactions within the Glu22-Gly29 segment play a critical role in forming and stabilizing the O-shaped structures. This conclusion is strongly supported by a comparative analysis of the structural preferences of the Ala21-Gly29 segment during the MD simulations performed at both pHs. At pH 8 (as well as at the neutral pH, when the Glu22 and Asp23 residues are deprotonated and negatively charged), the Ala21-Gly29 segment adopts well-stabilized, O-shaped structures. At pH 3 (when the Glu22 and Asp23 residues are protonated and uncharged) the Ω-shaped structures are not formed. It should be noted that the destruction of the Ω-shaped structure and high flexibility of the Ala21-Gly29 segment at pH 3 are associated with the protonation of the Glu22 and Asp23 residues at this pH. The revealed structural flexibility of the Ala21-Gly29 segment is well consistent with the data obtained by Massi et al.61 In that work it was shown that the Glu22Gln mutation in the Aβ(10–35) fragment causes larger structural flexibility of the mutated fragment at the neutral pH and room temperature when compared with the structural flexibility of the wild-type fragment. The important role of the electrostatic interactions of the Glu22, Asp23 and Lys28 residues shown in our work are also consistent with data of the recent work carried out for the Aβ(21–30) peptide at the neutral pH.68

The revealed dependence of the structural propensities of the Ala21-Gly29 segment on intra-segmental electrostatic interactions explains some structural effects caused by several pathological mutations of the Aβ protein at the neutral pH: the Arctic [Glu22Gly], Dutch [Glu22Gln], Italian [Glu22Lys] and Iowa [Asp23Asn]. In fact, these mutations suppress or disturb favorable electrostatic interactions within the Ala21-Gly29 segment and thus impede the formation of the Ω-shaped structures. Therefore, instead of forming the stable and relatively rigid Ω-shaped structures, the central segment adopts partially unfolded states that can initiate the subsequent structural changes. This assumption is consistent with the observations that the structural changes caused by the aforementioned pathological mutations increase the rate of nucleation and enhance the Aβ fibrilization, occurring at the neutral pH.69–73 On the other hand, our assumption on the electrostatic nature of the forming Ω-shaped structure is well correlated with data recently observed by Grant et al.74 suggesting that all disease-associated amino acid substitutions at Glu22 or Asp23 positions destabilize the turn-like structure of the Glu21-Ala30 segment of the Aβ protein that, in turn, causes familial forms of AD and cerebral amyloid angiopathy.

Thus, our data, taken together with the recent literature data, allowed us to suggest that any neutralization (by pH changing or mutations) of the charged aspartic (Glu22) and/or glutamic (Asp23) acid residues in the Aβ monomer can induce a partial unfolding of the Ala21-Gly29 segment and facilitate the amyloid oligomer and protofibril formations.

Role of structural organization of the Aβ40 core domain in the oligomerization and protofibril aggregation of the Aβ monomers.

Our analysis showed that during MD simulations performed for two different initial structures (A—the structure with a high α-helix content and B—a polyproline II structure) the conformational evolution of the Aβ40 core domain achieves rather steady pH-dependent states, exhibiting flexible, unstable helix-like structuration.

Figure 2, Tables 1 and 2 point to the existence of three structural zones within the Aβ40 core domain. Amino acid residues within Zones I and III prefer to form flexible and fluctuating helix-like structures (molten helixes) at both pHs, while the residues within Zone II have pronounced propensities to adopt rather stable structures at pH 8. Based on their structural properties, we called Zones I and III the molten (or transit) helical zones and Zone II the folded zone. The length of Zone I depends on pH; at pH 8 this zone is comprised of the Glu11-Phe20 residues, while at pH 3 this zone includes the Glu11-Val24 residues. The length of Zone II is also pH-dependent; at pH 8 this zone includes the Ala21-Gly29 residues, while at pH 3 it includes only the Gly25-Gly29 residues. The length of Zone III is pH-independent and includes the Ala30-Val36 residues. The pH-dependent structuration of the Aβ40 core domain associated with the aforementioned three zones is schematically presented in Figure 5. Below we discuss the roles that the length and structural properties of these zones can play in the processes of oligomerization and protofibril aggregation of the Aβ monomers.

The performed cluster analysis has shown that the nine residue segment, Ala21-Gly29, prefers to form the compactly-folded, Ω-shaped structures at pH 8, while at pH 3 the shorter, five-residue segment, Gly25-Gly29, can adopt relatively rigid, bend-like structures. Interestingly, at pH 3 (and in rare cases at pH 8) the Ala21-Val24 segment becomes unfolded and exhibits propensities to form fluctuating structures and thus can be considered as a continuation of the molten helical Zone I. These observations can be correlated with the experimentally observed different abilities of the Aβ monomers to aggregate into oligomeric and protofibril entities at different pHs. In fact, in vitro experiments have shown that the oligomeric and protofibril aggregation of the Aβ monomers can be induced by low pH and elevated temperature.13,35–39 The aggregation rate of the Aβ fibril formation is much faster at the acidic pH compared to the neutral pH.13,38,39 By combining our computational data with the known experimental data, we suggested that the protofibril aggregation of the Aβ proteins is associated with the diminishing length of the folded zone and with unfolding of the Ala21-Val24 segment. On the other hand, the formation of the compactly-folded, Ω-shaped structures by the Ala21-Gly29 residues is detrimental to the Aβ oligomerization.

Therefore, we suggested that the length (five, but not nine residues) and structure (bend-shaped, but not Ω-shaped) of the folded zone contribute to the protofibril aggregation of the Aβ proteins. The agreement between our model of the Aβ fibrilization and known experimental data6,8,9 can be further enhanced by the assumption that the flexible, unstable helix-like structures formed by the residues from the molten Zones I and III could be transformed into β-strand structures, when the Aβ monomers form fibrils. This assumption is consistent with the concept of “unstable helix” state of the Aβ protein10 and with the hypothesis11 that considers a “discordant” α-helix of the Lys16-Asp23 segment as strongly favorable for β-strand formation. Our assumption is also based on the solid-state NMR data,6,8,9 which suggest that the Aβ40 fibrilization is associated with the formation of β-strand structures within Glu11-Val24 and Ala30-Val40 segments. These β-strand structures are bridged by the Gly25-Gly29 segment, which adopts a bent structure.

Below we explain how fluctuating structures, adopted by the Glu11-Val24 and Ala30-Val36 residues, can be transformed into the β-strand structures. Let us assume that the process of this structural conversion has two phases. In the first phase, suitable fluctuating structures, adopted by the Glu11-Val24 and Ala30-Val36 residues, bridged by the Gly25-Gly29 segment, can occasionally form structural motifs resembling helical hairpins. The formation of such motifs is facilitated by: (1) the inherent preferences of the Glu11-Val24 and Ala30-Val36 segments to form fluctuating (molten) helix-like structural motifs; (2) the presence of a remarkable number of the hydrophobic residues within these motifs; (3) the occurrence of the bend-shaped structures adopted by the Gly25-Gly29 segment; and (4) the presence of internal conformational variability of the Aβ40 at the Gly25 and Gly29 positions. In the second phase, when the occasionally formed hairpins are hydrophobically collapsed, the transition of α-helices into β-strands can occur.

The proposed hydrophobic mechanism can be illustrated by the cylindrical diagram presented in Figure 6. As can be seen from this diagram, the distribution of the hydrophobic residues along two cylinders, presenting α-helices formed by the Glu11-Val24 and Val30-Val36 residues, is typical for the cases when α-helices connected by an inter-helical loop are complementarily packed.75–77 The character of the continuous hydrophobic clusters on the helical surfaces and length of the gap (Gly25-Gly29) between these clusters suggest that the hydrophobic residues of these α-helices have the possibility to be packed in a face-to-face fashion and, in such a manner, to form structures reminding helical hairpins.

According to this diagram, the continuous hydrophobic clusters can be formed on three sides of the helix, adopted by the Val30-Val36 segment, and on two sides of the helix, adopted by the Glu11-Val24 segment. Moreover, the seven-amino acid sequence, comprised of the Leu17-Val18-Phe19-Phe20-Ala21-Glu22-Asp23 residues (see Helix 1 on the Fig. 6), has a hydrophobic pattern, typical for the coiled coil structural motif.78,79 In this motif, the first and fourth positions (in our case, the Leu17 and Phe20 residues) must be occupied by the hydrophobic residues. These residues form the hydrophobic core of the super coil structure assembled from parallel or anti- parallel α-helices.78,79 Recently, it was found that the fifth and seventh residues (in our case, the Ala21 and Asp23) can have non-polar side chains.79 Thus, one can suggest that the coiled coil motif formed by the Leu17-Asp23 segment within the Aβ monomer and hydrophobic effect (providing direct contact of the corresponding hydrophobic clusters) are important elements of the Aβ oligomerization process. Such a process should involve the formation of the super coil structures, built from the parallel oriented helical segments comprised of the Leu17-Asp23 residues of several Aβ monomers. In this case, the Asp23 has to be buried in the hydrophobic environment. At pH 3, when Asp23 is in the protonated state, this should not be a problem. At pH 8 (as well as at the neutral pH ∼7), this is also possible when the Asp23 ionogenic group can form an ion pair with the ionogenic group of Lys28.

Through the diffusion-collision process of the Aβ monomers, the hydrophobic clusters can provide a mutual basis necessary for Aβ monomers to initiate oligomerization, driven by the hydrophobic interactions.18,80 This process can be followed by a transition of α-helices into β-strands forming the major structural motifs (β-sheets) typical for Aβ fibrils.6,8,9,12–15,22 Transition of the helical structures into the β-strand structures was suggested in several works.10–13,15,61 One of the possible reasons why the helical structures can be altered into the β-strand structures is discussed below.

Due to the oligomerization of hydrophobically collapsed Aβ40 monomers, the residues involved in the helical formations can become significantly isolated from the aqueous solvent and exposed to the protein-core-like medium. It may be reasonable to suggest that this new environment can promote the conversion of the unstable flexible α-helical structures into β-strands. The possible physicochemical basis for this conversion may be associated with alterations in a balance of intra-residual non-covalent (electrostatic) interactions (that determine conformational propensities of an amino acid residue in protein) when the polar (solvent) surroundings are replaced by a non-polar medium typical for the internal protein region.81–83 This effect assumes that amino acid residues buried within the protein-like media can have different preferences to adopt possible conformations compared to the conformational preferences of these residues when they are exposed to solvent at the protein-solvent interface. Our previous data82 suggest that amino acid residues located in the interior of proteins can have higher preferences to adopt extended, β-strand-like conformations compared to the residues located on the protein surface.

The proposed model of the Aβ oligomerization enriches the existing structural models of Aβ oligomerization and fibrillization. For example, one of the advanced structural models was suggested by Fezoui et al.84,85 for the de novo designed 38-residue helical hairpin peptide. When incubated in aqueous solvent at the neutral pH, this peptide can form the protease resistant fibrils that have the morphologic, structural and tinctorial properties of authentic amyloid fibrils formed by Aβ40 and Aβ42.86 In that work it was found that the partially folded intermediates, formed by the de novo designed peptide, containing the α-helix-turn-α-helix (αtα) motif, can mediate the initial stages of fibril formation. Our model suggests that the molten helical hairpins, occasionally adopted by the residues of the Aβ40 core domain, can initiate the Aβ fibril formation, followed by a transition of the helical zones into the β-strands typical for the Aβ fibrils. In addition, the proposed model addresses why and how the molten helical structures are transferred into the β-strand structures. Interestingly, the way these transient zones are marked within the Aβ40 sequence (by coding the amino acid sequence of the Glu11-Val24 and Ala30-Val36 segments, having inherent conformational propensities to adopt unstable fluctuating helix-like structures) is consistent with one observed in other short, intrinsically unfolded proteins.87

Methods

MD simulations protocol.

The MD simulations of the Aβ40 protein were performed starting from two initial structures (starting points). The first initial structure (referred to as the A structure) was taken as a representative from the family of Aβ40 structures derived from the NMR experiments;11 namely, it was the tenth structure of the 1BA4 file from the Brookhaven Data Bank. This structure suggests that the Asp1-His14 segment of Aβ40 is unstructured, while the Asp15-Val36 segment adopts α-helical conformation with a kink at Gly25-Asn27 residues. The second initial structure (referred to as the B structure) was taken with the backbone dihedral angles for each amino acid residue adopting the values (φ ≈ −69°, Ψ ≈ 149°); these dihedral angles are characteristic for the polyproline II structure (PPII). The PPII was chosen as the starting structure because all 20 types of amino acid residues can adopt this conformation50,51 and PPII can be easily transformed into other types of secondary structures.51 The MD simulations performed starting from the A and B initial structures we called the A and B runs, respectively.

The structural behavior of Aβ40 was studied at pH 3 and pH 8. At pH 8 all aspartic and glutamic acids in the Aβ40 were considered in deprotonated states, while at pH 3 these amino acid residues and histidines were protonated. All lysine and arginine residues of the Aβ40 were protonated at both pHs. Thus, at pH 8 the Glu and Asp residues were negatively charged, Arg and Lys residues were positively charged, and His had a zero charge. At the pH 3, the Glu and Asp residues were considered non-charged, whereas Arg, Lys and His residues were positively charged.

The SANDER module of the AMBER 7 package with an all-atom force field ff99 was used for the MD simulations.52,53 The LEaP module of this package53 was utilized to protonate/deprotonate the aforementioned residues. The initial Aβ40 structures were solvated in a periodic box of the TIP3P model water.54 The box size was chosen to provide not less than 9.0 Å from each wall to any atom of Aβ40.

All simulations were performed using periodic boundary conditions and the SHAKE algorithm55 at a constant temperature of 500° K using the Berendsen coupling algorithm (NTT = 1).56 The constant pressure MD simulations (NTP protocol)53 were performed with the 1 fs time step. To carry out the simulations at pH 8, positive counter ions, Na⁺, were added at the most negative regions of the electrostatic potential to neutralize the simulation system. It was done by mutually replacing the corresponding water molecules. Analogously, the negative counter ions, Cl⁻, were used to neutralize the simulation system at pH 3.

The electrostatic interactions were calculated by the Particle Mesh Ewald method57 implemented in SANDER. The van der Waals and electrostatic interactions were evaluated with a 9.0 Å cutoff value. The non-bonded pair list was updated every 100 steps. After the initial 1,000 steps of energy minimization, the system was equilibrated during 100 ps of the MD run with positional constraints. During the first 20 ps of the equilibration, the system was heated from 0 to 500° K. The positional constraints were gradually reduced from 50 to 0.5 kcal/(mol*Å) within the equilibration time.

The productive (without positional constraints) MD simulations were carried out at 10.9 ns and 30 ns for the A and B initial structures, respectively. Data generated during MD simulations were stored in trajectory files every 1 ps, providing 10,900 and 30,000 conformers for the A and B runs, respectively. Two trajectory files (MDA₃ and MDA₈) were generated during the A runs at pH 3 and pH 8, respectively. Analogously, the MDB3 and MDB₈ files were generated during the B runs at pH 3 and pH 8, respectively. Four representative structural sets, RSA₃ and RSA₈ as well as RSB₃ and RSB₈, were obtained from the corresponding MDA₃, MDA₈, MDB₃ and MDB₈ trajectory files by extracting 500 structures evenly distributed during the last 10 ns of the MD simulations.

All simulations were performed on the Beowulf computer cluster containing 32x nodes Atipa Dual-Xeon (32x Xeon 3.06 GHz and 32x Xeon 2.4 GHz). Data analysis was carried out on the SGI O2 workstation. The collected data were analyzed by the CARNAL module of AMBER as well as by the PROTABLE module and the graphic tools of the SYBYL software package (Tripos, Inc.).

Structural propensities (SP).

The involvement of each residue in the formation of secondary structure elements (SSE) was estimated by the Kabsh-Sander procedure58 incorporated in the SYBYL software package. This procedure allows one to assign the involvement of each amino acid residue in forming α-helix (H), isolated β-strand (B), hydrogen bonded β-strand (E), 3₁₀-helix (G), π-helix (I) and hydrogen bonded β-turn (T). Residues unassigned to any of the aforementioned SSE were considered to be in a random coil (C). The Kabsh-Sander procedure was performed for the RSA₈, RSA₃ and RSB₈, RSB₃ sets to calculate SSE profiles along the Aβ40 amino acid sequence for both A and B runs carried out at both considered pHs. The occupation percentages (or structural propensities) of the seven structural states (H, G, I, B, E, T and C) for each amino acid residue of Aβ40 were also calculated.

Structural cluster analysis.

The RSA₃ and RSA₈ as well as RSB₃ and RSB₈ sets were analyzed to determine the possible structural organization of the different segments of the Aβ40 sequence. For this purpose, a procedure for cluster analysis similar to one described earlier59,60 was used.

Structural cluster analysis was performed for several Aβ40 segments. For each cluster (comprising all conformers satisfying a given RMSD criterion), the average structure was calculated by the SYBYL software package. These average structures were energy-minimized to test the persistence of these structures at low temperatures. The minimization was performed by the SYBYL software package using the AMBER7 FF99 force field, distance-dependent dielectric function ϵ = 2r, and a gradient convergence value of 0.05 kcal/(mol Å) for termination of the minimization process. The minimized structures were compared (by RMSD calculated for the backbone heavy atoms) with the “ideal” α-helical, 3₁₀-helical, π-helical and β-strand structures. These “ideal” structures were set up by the backbone dihedral angles for each amino acid residue: φ = −57°, Ψ = −47° (for α-helix); φ = −50°, Ψ = −28° (for 3₁₀-helix); φ = −57°, Ψ = −70° (for π-helix); and φ = −139°, Ψ = 135° (for β-strand).

Hydrogen bond analysis.

The analysis of the hydrogen bonds (H-bonds) was carried out for the Glu22-Gly29 segment using the set of structures collected in the MDA₈ and MDB₈ trajectory file. This analysis was performed by the CARNAL module of the AMBER with the use of the 4.0 Å cut-off distances between the corresponding heavy atoms (CD for Glu22, CG for Asp23, NH and NZ for Lys28, NH and OG for Ser26 as well as NH for Val24, Gly25, Asn27 and Gly29) and the cut-off donor-hydrogenacceptor angle within 60° of linearity.

Conclusion

In this work, the pH-dependent structural features of the Aβ40 core domain were determined by the high temperature MD simulations, performed at pH ∼8 and pH ∼3. The obtained data combined with the known experimental data allowed us to describe the structural properties of the Aβ40 monomers and enrich existing models of Aβ oligomerization and fibrillization.

Analysis of the MD simulations data suggests the existence of three structural zones within the Aβ40 core domain: two molten zones (Zones I and III) and one folded zone (Zone II). At both considered pHs the amino acid residues within Zones I and III form flexible and fluctuating helix-like structures (molten helixes). In contrast, the amino acid residues within Zone II form rather stable structures at pH 8. The length of Zone I depends on the pH. At pH 8, this zone is comprised of the Glu11-Phe20 residues, while at pH 3 this zone includes the Glu11-Val24 residues. The length of Zone II is also pH dependent. At pH 8 this zone is comprised of nine residues (Ala21-Gly29) and at pH 3 it includes only five residues (Gly25-Gly29). At pH 3 (and in rare cases at pH 8), the Ala21-Val24 residues form fluctuating structures and thus can be considered as a part of the molten helical Zone I. The length of Zone III appears to be pH-independent and includes the Ala30-Val36 residues.

Combined analysis of the MD simulations and experimental data suggested that adopting the compactly-folded, Ω-shaped structures by the nine residue segment, Ala21-Gly29, blocks the Aβ oligomerization process. When this segment becomes partially unfolded (i.e., when the Ala21-Val24 residues form fluctuating structures) and when only five residues (Gly25-Gly29) of this segment are folded in the bend-like structures, the processes of Aβ oligomerization and fibrillization can occur.

Analysis of the flexible helical structures, formed within the molten zones (Zone I and Zone III), revealed the existence of the continuous hydrophobic clusters, which can be responsible for intra-molecular hydrophobic collapsing of the molten zones. In addition to this, we suggested that the formation of helical structures by the Leu17-Asp23 residues can be instrumental in inter-molecular hydrophobic collapsing of Aβ monomers and forming the super-coil structures, built from the parallel oriented helical segments that include the Leu17-Asp23 residues of several Aβ monomers. This conclusion is based on the fact that the Leu17-Asp23 segment has a hydrophobic pattern typical for the coiled coil structures. Our results suggested that helical structuration of the Leu17-Asp23 residues is possible when the Ala21-Gly29 segment is partially unfolded and the Ala21-Val24 residues from this segment form fluctuating helical structures. Finally, we described a physicochemical mechanism of how the hydrophobic collapsing can cause a transition of the molten helical zones into the β-strands typical for the Aβ fibrils.

The details of the Aβ40 structural organization described in this work and the proposed model of the Aβ oligomerization and fibrillization will be useful for further studies of possible mechanisms of the Aβ aggregation.

Figures and Tables

Figure 1 Dynamics behavior of the radii of gyration (Rg) of Aβ40 during MD simulations performed for (A and B) initial structures at both considered pHs. Notes: Plots of the radii of gyration calculated (in Angstrom) for backbone atoms (Cα, C, N) of Aβ40 at pH 8 and pH 3 are shown in the upper and lower parts of the figure, correspondingly. Colored curves correspond to the A (magenta) and B (blue) initial structures (see Methods).

Figure 2 Percentage (%) of involvement of the amino acid residues within the Aβ40 sequence in forming the secondary structural elements (structural propensity) during the last 10 ns of MD simulations at pH 8: (A and B) present secondary structure sets determined by the analyses of the RSA₈ and RSB₈ structural sets, correspondingly. Notes: The secondary structure elements were depicted by different colors: α-helix (green), 3₁₀-helix (blue), β-turn (yellow) and random coil (red).

Figure 3 The trace of the C_α-atoms of the average Ω-shaped structure formed by the Ala21-Gly29 segment in the stable state at pH 8.

Figure 4 A typical three-dimensional structure formed by the Glu22-Gly29 segment in the stable state at pH 8. Notes: Observed H-bonds between polar groups are shown by dash-lines. CD, CG, OG and NZ note the heavy atoms of the donor-acceptor groups of the interacting residues.

Figure 5 Schematic presentation of the major structural states of the Glu11-Val36 segment of the Aβ40 core domain considered at pH 8 and pH 3. The rectangular blocks along the sequence designate the flexible and fluctuating helix-like structural modes: Glu11-Phe20 (Helix 1′) at pH 8; Glu11-Val24 (Helix 1) at pH 3, and Ala30-Val36 (Helix 2) at both pHs. The Ala21-Gly29 residues at pH 8 form the Ω-shaped structure (comprised of about 84% of the MD generated structures). The Gly25-Gly29 residues at both pHs form a bend-shaped structure.

Figure 6 Helical net layout of the Glu11-Gly37 segment. Notes: The sequence is presented by the net diagram typical for two α-helices, formed by the Glu11-Val24 (Helix 1) and Ala30-Val36 (Helix 2) segments. The residues forming the continuous hydrophobic clusters are marked by dark circles. The residues forming the bend structures (Gly25-Gly29) are marked by the hexagons. The numbers present the positions of the corresponding amino acid residues in the Aβ40 sequence.

Table 1 The structural propensities (occupation percentage) of amino acid residues within Glu11-Val39 segment to be involved in the formation of secondary structure elements revealed from the RSA₈ and RSA₃ structural sets at the last 10 ns of the MD simulations

	RSA8				RSA3
	G	H	T	C	G	H	T	C
Glu11	31	18	30	21	30	28	29	13
Val12	32	25	39	4	33	31	27	8
His13	29	24	43	3	27	29	26	17
His14	18	25	48	8	24	23	30	22
Gln15	13	17	52	17	23	27	26	24
Lys16	23	14	41	22	28	24	30	17
Leu17	38	20	34	8	29	31	30	10
Val18	38	20	31	10	20	34	37	8
Phe19	34	18	25	23	27	38	28	6
Phe20	17	13	38	32	28	36	31	5
Ala21	9	4	37	49	29	32	32	6
Glu22	3	1	36	60	20	26	37	17
Asp23	1	0	0	98	13	18	36	32
Val24	1	0	1	98	9	8	43	40
Gly25	1	0	1	98	7	7	26	59
Ser26	3	1	8	87	21	9	36	34
Asn27	4	2	16	78	21	11	34	34
Lys28	5	3	17	74	22	13	34	31
Gly29	19	10	27	43	12	13	30	45
Ala30	27	15	31	26	32	15	32	21
Ile31	33	20	33	13	34	14	39	13
Ile32	31	27	32	8	33	19	33	14
Gly33	27	25	26	21	22	20	39	17
Leu34	32	22	30	15	29	24	37	10
Met35	28	18	39	15	26	22	43	9
Val36	16	10	51	23	17	17	49	16
Gly37	3	4	38	54	3	10	41	44
Gly38	0	1	14	85	1	1	23	75
Val39	0	0	5	95	0	0	8	91

Notes: G, 3₁₀-helix; H, α-helix; T, β-turn and C, random coil.

Table 2 The structural propensities (occupation percentage) of amino acid residues within Glu11-Val39 segment to be involved in the formation of secondary structure elements revealed from the RSB8 and RSB3 structural sets at the last 10 ns of the MD simulations RSA₈ RSA₃

	G	H	T	C	G	H	T	C
Glu11	43	11	36	10	19	31	13	37
Val12	45	22	28	4	23	24	27	27
His13	48	24	22	5	24	20	32	23
His14	33	27	34	6	21	22	34	23
Gln15	30	21	22	28	32	21	29	18
Lys16	41	14	32	12	34	21	37	9
Leu17	43	26	25	6	36	31	27	6
Val18	42	31	24	3	28	37	26	8
Phe19	37	31	28	3	38	40	20	2
Phe20	25	27	43	5	27	41	29	3
Ala21	14	13	58	15	28	35	28	9
Glu22	2	4	64	31	20	30	38	11
Asp23	0	0	0	100	16	26	44	14
Val24	0	0	1	99	9	17	53	20
Gly25	0	0	1	99	6	16	38	40
Ser26	0	0	7	92	22	12	46	18
Asn27	0	0	10	89	23	10	55	10
Lys28	1	1	12	86	20	10	44	24
Gly29	15	3	18	63	13	7	32	46
Ala30	49	8	27	16	31	12	30	26
Ile31	52	16	25	7	34	13	34	19
Ile32	49	22	22	6	31	23	28	17
Gly33	25	24	41	9	22	23	31	23
Leu34	28	25	38	8	32	23	33	11
Met35	26	18	47	9	30	22	38	9
Val36	19	12	52	17	26	14	45	14
Gly37	3	6	40	51	9	9	43	36
Gly38	1	0	18	81	2	2	37	59
Val39	0	0	9	91	1	1	12	86

Notes: G, 3₁₀-helix; H, α-helix; T, β-turn and C, random coil.

Table 3 Percentage (%) of helical structures adopted by five tetrapeptide segments of Aβ40 at pH 8 and pH 3

	pH 8			pH 3
Segment	Type of helix	RMSD^a	% (%A + %B)^b	RMSD^a	% (%A + %B)^b
E11-H14
	α	0.3	95.7 (48.3 + 47.4)	0.7	87.8 (45.1 + 42.7)
	310	0.7	4.2 (1.7 + 2.5)	0.4	10.0 (4.0 + 6.0)
H14-L17
	α	0.3	74.8 (41.6 +33.2)	0.3	82.3 (39.7 + 42.6)
	310	0.9	20.2 (7.3 + 12.9)	1.1	14.8 (7.8 + 7.0)
L17-F20
	α	0.4	88.1 (43.2 + 44.9)	0.4	85.9 (43.8 + 42.1)
	310	0.6	9.1 (4.2 + 4.9)	1.3	13.6 (6.1 + 7.5)
A30-G33
	α	0.3	90.4 (43.7 + 46.7)	0.3	81.5 (43.1 + 38.4)
	310	0.7	7.7 (5.6 + 2.1)	0.6	15.6 (5.6 + 10.0)
G33-V36	α	0.3	91.8 (45.5 + 46.3)	0.3	91.1 (45.6 + 45.5)

Notes: ^a-Numbers show RMSD (in Angstrom) between the heavy atoms of the main chain of the considered tetrapeptides and the analogous atoms of helixes. ^b-% before parenthesis is overall percentage of structures that were assigned to the given cluster; %A and %B—percentage of structures within the given cluster that were generated during the MD simulations starting from the A and B initial structures, correspondingly.

Table 4 The percentage (%) of structures assigned to the most populated clusters formed by the Ala21-Gly29 segment and overall description of the structures formed by the Ala21-Val24 residues

pHs	Cluster's number	Ala21-Gly 29 %	Ala21-Val24 structure
pH 8	1	84	hook
	2	5	hook
	3	4	β-strand
	4	3	helix-like
pH 3	5	39	α-helix
	6	14	α-helix
	7	11	β-turn
	8	6	3/10-turn

Notes: The population percentage (%) of the clusters was determined using RMSD ≤ 1.6 Å as the criterion of structural similarity. For each cluster, structures formed by the Ala21-Val24 residues are described by their appearance and/or due to their RMSD closeness to the considered structures.

Table 5 Percentage of the cases (%), in which the hydrogen bonds (H-bonds) between the donor-acceptor groups of the residues within the Glu22-Gly29 segment are formed

Amino acid pairs	Heavy atoms of the donor-acceptor groups	H-bonds (%)
Glu22-Lys28	CD…NZ	51
Asp23-Val24	CG…NH	59
Asp23-Gly25		89
Asp23-Ser26		70
Asp23-Asn27		76
Asp23-Lys28		68
Asp23-Gly29		58
Asp23-Ser26	CG…OG	24

Note: %—the percentage of cases of forming the given hydrogen bonds when the Gl22-Gly29 segment is in the stable state.

Acknowledgements

We thank Dr. L. Kinarsky (University Nebraska Medical Center) and Dr. V. Uversky (Indiana University) for helpful remarks. We acknowledge the use of the UNMC Bioinformatics Core Facility partially supported by NRI Nebraska Research Initiative, NIH Cancer Center Support Grant, NIH BRIN Nebraska Training Network in Functional Genomics and NIH grant 1-PN1 EY016593-01.